Strategy Repair in Reachability Games

We introduce Strategy Repair, the problem of finding a minimal amount of modifications to turn a strategy for a reachability game from losing into winning. The problem is relevant for a number of settings in Planning and Synthesis, where solutions essentially correspond to winning strategies in a suitably defined reachability game. We show, via reduction from Vertex Cover, that Strategy Repair is NP-complete and devise two algorithms, one exact and exponential and one polynomial but suboptimal, which we compared experimentally. The reported experimentation includes some heuristics for strategy modification, which proved crucial in dramatically improving performance.